Rarefaction throttling effect: Influence of the bend in micro-channel gaseous flow

Abstract

Micro-bends are frequently encountered in micro-electro-mechanical systems (MEMS) as a basic unit of complex geometry. It is essential for a deep understanding of the rarefied gas flow through bent channel. In this paper, a two-dimensional pressure-driven gas flow in a micro-channel with two bends is investigated by solving the Bhatnagar-Gross-Krook kinetic equation via the discrete velocity method in the slip and transition flow regimes. The results show that the mass flow rate (MFR) through the bent channel is slightly higher than that in the straight channel in the slip flow regime but drops significantly as the Knudsen number increases further. It is demonstrated that the increase of MFR is not due to the rarefaction effect but to the increase in cross-section of the bent corners. As the rarefaction effect becomes more prominent, the low-velocity zones at the corners expand and the gas flow is "squeezed" into the inner corner. The narrowed flow section is similar to the throttling effect caused by the valve, and both the changes in MFRs and the pressure distribution also confirm this effect. The classical Knudsen minimum changes due to this "rarefaction throttling effect". The Knudsen number at which the minimum MFR occurs gradually increases with the bend angle, and finally disappears in the transition flow regime. In addition, the onset of rarefaction throttling effect shifts to a smaller Knudsen number with a lower tangential momentum accommodation coefficient.

Rarefied flow separation in microchannel with bends

“…Small recirculation at the bends can be deduced from the velocity profiles obtained in the numerical simulation of the Navier-Stokes equations with the first-order slip velocity boundary condition (Raju & Roy 2004). However, the others explicitly confirmed that no trace of flow separation was found using the DSMC method (Wang & Li 2004) and the discrete velocity method (DVM) of solving the linearised kinetic equations (Sharipov & Graur 2012;Liu et al 2018). Table 1 further shows that the mass flow rate ratio α is reported in the literature in a rather scattered fashion.…”

“…flow in a straight microchannel has been extensively investigated (Sharipov & Seleznev 1998;Sazhin 2009;Titarev 2012a,b;Varoutis, Day & Sharipov 2012), only a few experimental (Lee, Wong & Zohar 2001;Varade et al 2015) and numerical (Raju & Roy 2004;Wang & Li 2004;Agrawal, Djenidi & Agrawal 2009;Sharipov & Graur 2012;White et al 2013;Kulakarni, Shterev & Stefanov 2015;Rovenskaya 2016;Liu et al 2018) studies have been carried out for rarefied gas flows through a microchannel with bends, which are often encountered in miniaturised devices. One of the typical phenomena in bent channels is flow separation, which is important for many engineering applications and has been studied extensively in the continuum limit (Bradshaw & Wong 1972).…”

Free-molecular and near-free-molecular gas flows over backward facing steps

“…Motivated by the overwhelming complexity of channels networks contained in microfluidic chips (Thorsen, Maerkl & Quake 2002), the study of heat and mass transfer phenomena in non-straight channel geometries has become the focus of several works. In the context of rarefied gas flows, these have included, among others, studies on the effects of channels bending (Sharipov & Graur 2012;Liu et al 2018), gradual section expansion (Naris, Tantos & Valougeorgis 2014;Graur et al 2015;Hemadri, Parade & Bhandarkar 2016;Tatsios et al 2017) and geometrical irregularities, including sudden expansion and contraction (Agrawal, Djenidi & Antonia 2005;Gat, Frankel & Weihs 2008;Hong, Zhen & Yang 2008;Varade, Agrawal & Paradeep 2014).…”

Gaseous slip flow affected by inclined low magnetic field using second‐order boundary conditions

“…Dongari et al studied the pressure distribution for compressible gaseous flow. Liu et al investigated the rarefication effect for gaseous slip flow in a two‐dimensional microchannel with two bends in the slip and transition flow regimes. Duan studied the effect of Poiseuille number for slip flow through a circular and noncircular microchannel.…”